I drew some comics to help me cope with Boston drivers, the souls of whom are black as pitch. They live here: http://bostondrivingschool.tumblr.com/
A finite number of lines are dropped onto the plane. How many more lines must be added to ensure that every enclosed region of the plane is triangular? Is this possible?
Three gods A, B, and C are called, in no particular order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for yes and no are da and ja, in some order. You do not know which word means which. (via)
The integer 8 can be written as the sum of two squares of integers, m^2 + n^2, in four ways, when (m, n) is (2, 2), (2, -2), (-2, 2), or (-2, -2). The integer 7 can’t be written at all as the sum of such squares. Over a very large collection of integers from 1 to n, the average number of ways an integer can be written as the sum of two squares approaches π. Why? (via)
Basically what it sounds like.
If you aren’t concerned about unleashing potentially bright, flashing, animated mayhem, you can play with it here.
Here are some fun images we’ve made with it: